TSTP Solution File: SET063+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 06:33:21 EDT 2022
% Result : Theorem 0.78s 1.01s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 19:51:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.78/1.01 (* PROOF-FOUND *)
% 0.78/1.01 % SZS status Theorem
% 0.78/1.01 (* BEGIN-PROOF *)
% 0.78/1.01 % SZS output start Proof
% 0.78/1.01 Theorem corollary_of_null_class_is_subclass : (forall X : zenon_U, ((subclass X (null_class))->(X = (null_class)))).
% 0.78/1.01 Proof.
% 0.78/1.01 assert (zenon_L1_ : forall (zenon_TX_bt : zenon_U), (~(subclass (null_class) zenon_TX_bt)) -> False).
% 0.78/1.01 do 1 intro. intros zenon_H2c.
% 0.78/1.01 generalize (subclass_defn (null_class)). zenon_intro zenon_H2e.
% 0.78/1.01 generalize (zenon_H2e zenon_TX_bt). zenon_intro zenon_H2f.
% 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2c; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ].
% 0.78/1.01 apply (zenon_notallex_s (fun U : zenon_U => ((member U (null_class))->(member U zenon_TX_bt))) zenon_H32); [ zenon_intro zenon_H33; idtac ].
% 0.78/1.01 elim zenon_H33. zenon_intro zenon_TU_ca. zenon_intro zenon_H35.
% 0.78/1.01 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.78/1.01 generalize (null_class_defn zenon_TU_ca). zenon_intro zenon_H38.
% 0.78/1.01 exact (zenon_H38 zenon_H37).
% 0.78/1.01 exact (zenon_H2c zenon_H31).
% 0.78/1.01 (* end of lemma zenon_L1_ *)
% 0.78/1.01 assert (zenon_L2_ : forall (zenon_TX_bt : zenon_U), (forall U : zenon_U, ((member U zenon_TX_bt)->(member U (null_class)))) -> (~(subclass zenon_TX_bt (null_class))) -> False).
% 0.78/1.01 do 1 intro. intros zenon_H39 zenon_H3a.
% 0.78/1.01 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H3b.
% 0.78/1.01 generalize (zenon_H3b (null_class)). zenon_intro zenon_H3c.
% 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H39 ].
% 0.78/1.01 exact (zenon_H3e zenon_H39).
% 0.78/1.01 exact (zenon_H3a zenon_H3d).
% 0.78/1.01 (* end of lemma zenon_L2_ *)
% 0.78/1.01 apply NNPP. intro zenon_G.
% 0.78/1.01 apply (zenon_notallex_s (fun X : zenon_U => ((subclass X (null_class))->(X = (null_class)))) zenon_G); [ zenon_intro zenon_H3f; idtac ].
% 0.78/1.01 elim zenon_H3f. zenon_intro zenon_TX_bt. zenon_intro zenon_H40.
% 0.78/1.01 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H3d. zenon_intro zenon_H41.
% 0.78/1.01 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H3b.
% 0.78/1.01 generalize (zenon_H3b (null_class)). zenon_intro zenon_H3c.
% 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H39 ].
% 0.78/1.01 exact (zenon_H3a zenon_H3d).
% 0.78/1.01 generalize (extensionality (null_class)). zenon_intro zenon_H42.
% 0.78/1.01 generalize (zenon_H42 zenon_TX_bt). zenon_intro zenon_H43.
% 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ].
% 0.78/1.01 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H2c | zenon_intro zenon_H3a ].
% 0.78/1.01 apply (zenon_L1_ zenon_TX_bt); trivial.
% 0.78/1.01 apply (zenon_L2_ zenon_TX_bt); trivial.
% 0.78/1.01 apply zenon_H41. apply sym_equal. exact zenon_H45.
% 0.78/1.01 Qed.
% 0.78/1.01 % SZS output end Proof
% 0.78/1.01 (* END-PROOF *)
% 0.78/1.01 nodes searched: 25708
% 0.78/1.01 max branch formulas: 2260
% 0.78/1.01 proof nodes created: 1190
% 0.78/1.01 formulas created: 101486
% 0.78/1.01
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